Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

13.8K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
13.8K
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

1.5K
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
1.5K
Types of Coprecipitation01:10

Types of Coprecipitation

6.8K
Coprecipitation is the contamination of a precipitate by otherwise soluble species and occurs via different processes. In colloidal precipitates, coprecipitation occurs via surface adsorption. For instance, barium sulfate has a primary layer of adsorbed barium ions and a secondary layer of nitrate counterions. This results in contamination of the precipitate by barium nitrate.
Sometimes, ions in a crystal lattice can undergo isomorphous replacement by inclusions of similar charge and size. For...
6.8K
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

16.9K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
16.9K
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

4.1K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
4.1K
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

8.3K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
8.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Site and bond percolation in linearly distorted triangular and square lattices.

Physical review. E·2026
Same author

Percolation of random compact diamond-shaped systems on the square lattice.

Physical review. E·2026
Same author

Bond percolation in distorted square and triangular lattices.

Physical review. E·2025
Same author

Comparative Evaluation of Dissolution Performance in a USP 2 Setup and Alternative Stirrers and Vessel Designs: A Systematic Computational Investigation.

Molecular pharmaceutics·2024
Same author

Particle Size, Dose, and Confinement Affect Passive Diffusion Flux through the Membrane Concentration Boundary Layer.

Molecular pharmaceutics·2023
Same author

Percolation in two-species antagonistic random sequential adsorption in two dimensions.

Physical review. E·2023

Related Experiment Video

Updated: Mar 8, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

7.2K

Percolation in finite matching lattices.

Stephan Mertens1, Robert M Ziff2

  • 1Institut für Theoretische Physik, Otto-von-Guericke Universität, PF 4120, 39016 Magdeburg, Germany and Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, New Mexico 87501, USA.

Physical Review. E
|January 14, 2017
PubMed
Summary

We found a simple formula connecting cluster counts and wrapping probabilities in 2D percolation. This helps accurately estimate the critical density, offering a new view on existing methods.

More Related Videos

Patterning of Microorganisms and Microparticles through Sequential Capillarity-assisted Assembly
10:17

Patterning of Microorganisms and Microparticles through Sequential Capillarity-assisted Assembly

Published on: November 4, 2021

3.7K
The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

9.9K

Related Experiment Videos

Last Updated: Mar 8, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

7.2K
Patterning of Microorganisms and Microparticles through Sequential Capillarity-assisted Assembly
10:17

Patterning of Microorganisms and Microparticles through Sequential Capillarity-assisted Assembly

Published on: November 4, 2021

3.7K
The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

9.9K

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Network Science

Background:

  • Percolation theory studies the formation of connected clusters in random systems.
  • Understanding critical phenomena, like the percolation threshold, is crucial in various scientific fields.
  • Existing methods for approximating the percolation threshold have limitations.

Purpose of the Study:

  • To derive a new, exact relation for two-dimensional percolation.
  • To generalize a classical result by Sykes and Essam.
  • To provide a method for accurately determining the critical density.

Main Methods:

  • Derivation of an exact mathematical relation.
  • Analysis of percolation on periodic lattices of arbitrary size.
  • Generalization of existing theoretical frameworks.

Main Results:

  • An exact, simple relation between average cluster number and wrapping probabilities.
  • The relation is valid for periodic lattices of any size.
  • The derived relation facilitates precise approximation of the critical density.

Conclusions:

  • The new relation offers a simplified approach to percolation analysis.
  • It provides a novel perspective on methods for threshold approximation.
  • This work advances the understanding of critical phenomena in 2D systems.